Stargirl co-creator has revealed that talks involving an Arrowverse crossover have already happened.

Geoff Johns, Stargirl co-creator has gone on record to say that a potential crossover between the DC Universe original series and The CW’s Arrowverse is soon to become a reality.
When asked about the possibility of a Stargirl/Arrowverse crossover in conversation with CBR Johns said:
“We’re completely open to it. There’s so many possibilities. You know, clearly, we’re set on Earth-2, so we’re on our own Earth, much like the comic books. We’re set on Earth-2, and it gives us the room to tell our history and story, but also the opportunity in the future to do anything in the comic books or to always cross over with other places. Conversations have been had, but it’s all of matter of when it makes sense and if we have the best story.”
So, it’s confirmed that the talks have taken place and it’s also worth pointing out that CW picked up the broadcast rights for the series prior to its premiere. Under this deal, Stargirl first releases new episodes on DC Universe then airs on The CW the following Tuesday night.
This means that the two are already sharing the show, so they have equal stakes. On top of this, Stargirl has already featured in The CW’s “Crisis On Infinite Earths” five-show crossover.
It was only a brief appearance, the Seven Paragons had just restored the Arrowverse’s multiverse and the camera cut to some of the different earths that had been saved, among these we saw Stargirl’s home, Earth-2.
A number of similar universes were combined into one now dubbed Earth-Prime, a universe that is now home to Supergirl, Arrow, The Flash, DC Legends of Tomorrow and Batwoman. This means crisis has made it even more likely that we will see Stargirl crossover with the Arrowverse.
The Arrowverse is not planning for a major crossover event to take place next year due to the global pandemic and the regular fall season have all been moved back to January 2021 release date.
Supergirl is also being held back until midseason due to lead actress, Melissa Benoist’s pregnancy. Which obviously prevents Supergirl from taking part in any crossover.